# Revision problem. Chapter 18 problem 37 page 612. Suppose you point a pinhole camera at a 15m tall tree that is 75m away.

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1 Revision problem Chapter 18 problem 37 page 612 Suppose you point a pinhole camera at a 15m tall tree that is 75m away. 1

2 Optical Instruments Thin lens equation Refractive power Cameras The human eye Combining lenses Resolution 2

3 Optical Instruments - continued Optical imaging and color in medicine Integral part of diagnosis 3

4 Thin lens equation Instead of using ray tracing, we can use similar triangles to find the relationship between f, s and s 4

5 Thin lens equation Magnification triangles: m h h s s 5

6 Thin lens equation Focusing triangles: h s f h f 6

7 Thin lens equation Combining h s f s h f s 1 s f 1 1 s sf f s 7

8 Thin lens equation Focal length, f Distance from object to lens, s Distance from image to lens, s 1 f 1 s 1 s 8

9 Object distance, s Sign conventions is always positive for this course. Focal length, f is positive for converging lens, or concave mirror Is negative for diverging lens or convex mirror Magnification, M, and image height, h are positive when image is upright are negative when image is inverted 9

10 Image distance s Sign conventions Is positive for real images Is negative for virtual images 10

11 Sign Conventions for Lenses and Mirrors 11 Slide 19-11

12 Magnification Now use a sign convention, to indicate whether image is upright (positive) or inverted (negative) M h h s s 12

13 Refractive power A thicker lens will refract light at a larger angle and have a shorter focal length, f. We define the refractive power, P, as P 1 f Measured in diopters, 1D=1m -1 13

14 Refractive power of lenses in contact If two lenses are touching (or at least, very close), their refractive powers add. Useful for lenses which are close together such as corrective eye lenses P total P P 1 2 Measured in diopters, 1D=1m -1 14

15 Camera Simple single lens camera. Image is focused by a convex lens Shutter used to allow the light into the camera Recorded on CCD (used to be photosensitive paper, 35mm in width) 15

16 Camera CCD (Charge Coupled Device) is a 2D array of 1to >20 million pixels each of which is a photosensitive semiconductor with color filter 16

17 Focusing achieved by moving the lens towards or away from the image. Camera Exposure is controlled by changing the diameter of an iris behind the lens and the shutter time 17

18 Camera exposure Exposure is related to the amount of light which is recorded. Controlled by shutter speed and iris size Shutter speed is the time the shutter is open. Needs to be shorter for fast moving images 18

19 Shutter speed is the time the shutter is open. Camera exposure Needs to be shorter for fast moving images Expressed as fractions of a second 1/500s to 1/30s 19

20 Camera exposure Iris size controls the effective diameter of the lens Measured as the f-number, the ratio of the diameter of the lens, d, and the focal length f number Focal length, f is fixed, and light intensity goes as area, (d 2 ), or 1/(f-number) 2 Labeled as f-stops on a camera f d 20

21 Human Eye Focusing by the fixed cornea, and the variable lens Exposure controlled by the iris Recorded by the retina which contains photosensitive cells 21

22 Human Eye Focusing The cornea acts as a fixed lens. Corrections to the focusing applied by stretching the ciliary muscles to curve the lens, called accommodation 22

23 Human Eye Focusing Far point lens muscles relaxed longest focal length Near point lens muscles fully contracted, shortest focal length 23

24 Corrective lenses Two common types of conditions require corrective lenses Myopia or near sightedness rays converge in front of the retina when the lens muscles are relaxed Hyperopia or far sightedness rays converge behind the retina when the lens muscles are relaxed 24

25 Add a concave lens to diverge the light rays (negative focal length) This increases the far point Correcting Myopia 25

26 Add a convex lens Correcting Hyperopia Occurs when the eye is about 50 years old, and the lens becomes less elastic, and cannot curve. 26

27 Simple Magnifying lens Increases the apparent size of an object. Angular size for the magnified object is now h tan f 27

28 Simple Magnifying lens Increases the apparent size of an object. Compare the angular size at near point and for the magnified object Magnifies up to 20 M magnified near h f h 25cm magnified near 25cm f 28

29 Compound Microscope Simplest form contains two lenses Objective lens to create real image Eyepiece lens to magnify real image 29

30 Microscope Magnification from the objective lens M obj s s f L obj 30

31 Microscope Magnification from the eyepiece lens M eye 25cm f eye 31

32 Microscope Total magnification is the product of the two M total M obj M eye f L obj 25cm f eye 32

33 Telescope Two stage magnification, but with weaker objective lens 33

34 Telescope We want the angular magnification M eye obj 34

35 Objective lens angle Telescope obj f h obj 35

36 Eyepiece lens angle Telescope eye f h eye 36

37 Telescope magnification Total magnification M eye obj f f obj eye 37

38 Reflecting Telescope Need large aperture to capture more light large objective lens. Easier to make a mirror than a lens, Newton invented a reflecting telescope. 38

39 Resolution of optical instruments Imperfections in the lens are called aberrations Two main types Spherical aberration poor focusing Chromatic aberration color dispersion n(λ) 39

40 Correcting aberrations Spherical aberration remove the edges of the lens, using a smaller iris, but reduces image intensity Chromatic aberration use 2 lenses 40

41 Resolution from the wave model Telescopes, microscopes and lenses all have dimensions >> λ Images do not, however, when the instruments are used at their limits of resolution 41

42 Resolution from the wave model To separate two circular images, we would get 2 circular diffraction patterns Airy disk with ring fringes. The central disk has a radius D 42

43 Telescope Resolution Called Rayleigh s criterion, relates the angular resolution α, wavelength, λ, and object lens diameter D 43

44 Resolution of a Microscope At the object end of a microscope, the angular separation, θ min, and minimum resolvable distance, d min will be min 1.22 D d min f min 1.22f D 44

45 Resolution of a Microscope We replace D with 2f tanφ, which is nearly 2f sinφ. d min 0.61 sin 45

46 Resolution of a Microscope Some microscopes use a transparent oil which decreases the λ, and decreases the minimum resolution d min 0.61 n sin o 46

47 d Resolving power of a Microscope The resolving power of a microscope is defined by min RP 0.61 o NA Where NA is the numerical aperture NA nsin 47

48 Resolving power of a Microscope Values of the numerical aperture are around 1 for an immersion microscope, so the resolving power of a microscope can be as small as 0.5λ, half the wavelength of light. Smaller wavelengths can be obtained by using electron microscopes, where the object is irradiated with beams of electrons, to get from 2000x magnification to x1,000,000x 48

49 Thin lens equation Refractive power Cameras The human eye Combining lenses Resolution Summary 49

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